RCTs on masking

As far as I am aware, to date (23. IX. 2021) there have been two controlled trials on masking to reduce spread of SARS-CoV-2.

The Impact of Community Masking on COVID-19: A Cluster-Randomized Trial in Bangladesh
Conduced in rural Bangladesh November 2020 to April 2021, published September 1, 2021

Effectiveness of Adding a Mask Recommendation to Other Public Health Measures to Prevent SARS-CoV-2 Infection in Danish Mask Wearers
Conducted in Denmark, April and May 2020, published March 2021

The Danish study had two arms: face masks, no face masks. "At baseline and in weekly follow-up e-mails, participants in both groups were encouraged to follow current COVID-19 recommendations from the Danish authorities" which were "social distancing (including in shops and public transportation, which remained open), limiting the number of persons seen, frequent hand hygiene and cleaning". The study found no statistically significant reduction in infection between the two groups. What is significant is that treatment of both groups was the same, including weekly contact, and the only variable was one group was wearing face masks. The study was mostly occurring during a time period when restaurants and cafes were closed (till 18. May).

The Bangladesh study had three arms: medical masks, cloth masks and no masks. Significantly, only the groups given to wear masks received any intervention. "All intervention arms received free masks, information on the importance of masking, role modeling by community leaders, and in-person reminders for 8 weeks. The control group did not receive any interventions." The differing treatment of control vs intervention groups means that the main conclusion which can be drawn is that campaigns to encourage mask wearing change the behavior of people, as also adherence to physical distancing measures was found to be 5% higher in the intervention villages. The confidence intervals on symptomatic seroprevalence (Table A7) do not exclude no effect, while confidence intervals for COVID19 symptoms (Table A8) are certain there is a small effect. There is indication that whatever effect masks do have, surgical masks are superior to cloth masks.